1,751 research outputs found
Separation-Sensitive Collision Detection for Convex Objects
We develop a class of new kinetic data structures for collision detection
between moving convex polytopes; the performance of these structures is
sensitive to the separation of the polytopes during their motion. For two
convex polygons in the plane, let be the maximum diameter of the polygons,
and let be the minimum distance between them during their motion. Our
separation certificate changes times when the relative motion of
the two polygons is a translation along a straight line or convex curve,
for translation along an algebraic trajectory, and for
algebraic rigid motion (translation and rotation). Each certificate update is
performed in time. Variants of these data structures are also
shown that exhibit \emph{hysteresis}---after a separation certificate fails,
the new certificate cannot fail again until the objects have moved by some
constant fraction of their current separation. We can then bound the number of
events by the combinatorial size of a certain cover of the motion path by
balls.Comment: 10 pages, 8 figures; to appear in Proc. 10th Annual ACM-SIAM
Symposium on Discrete Algorithms, 1999; see also
http://www.uiuc.edu/ph/www/jeffe/pubs/kollide.html ; v2 replaces submission
with camera-ready versio
Computational Geometry Column 43
The concept of pointed pseudo-triangulations is defined and a few of its
applications described.Comment: 3 pages, 1 figur
Kinetic collision detection between two simple polygons
AbstractWe design a kinetic data structure for detecting collisions between two simple polygons in motion. In order to do so, we create a planar subdivision of the free space between the two polygons, called the external relative geodesic triangulation, which certifies their disjointness. We show how this subdivision can be maintained as a kinetic data structure when the polygons are moving, and analyze its performance in the kinetic setting
Design and loading of dragline buckets
Draglines are an expensive and essential part of open cut coal mining. Small improvements in performance can produce substantial savings. The design of the bucket and the way in which it fills with overburden are very important to the overall dragline performance. Here we use a numerical model to simulate this filling process and to differentiate between the flow patterns of two different buckets. Extensions to the model are explored
New Geometric Data Structures for Collision Detection
We present new geometric data structures for collision detection and more, including: Inner Sphere Trees - the first data structure to compute the peneration volume efficiently. Protosphere - an new algorithm to compute space filling sphere packings for arbitrary objects. Kinetic AABBs - a bounding volume hierarchy that is optimal in the number of updates when the objects deform. Kinetic Separation-List - an algorithm that is able to perform continuous collision detection for complex deformable objects in real-time. Moreover, we present applications of these new approaches to hand animation, real-time collision avoidance in dynamic environments for robots and haptic rendering, including a user study that exploits the influence of the degrees of freedom in complex haptic interactions. Last but not least, we present a new benchmarking suite for both, peformance and quality benchmarks, and a theoretic analysis of the running-time of bounding volume-based collision detection algorithms
Kinetic collision detection for balls rolling on a plane
This abstract presents a first step towards kinetic col- lision detection in 3 dimensions. In particular, we design a compact and responsive kinetic data struc- ture (KDS) for detecting collisions between n balls of arbitrary sizes rolling on a plane. The KDS has size O(n log n) and can handle events in O(log n) time. The structure processes O(n2) events in the worst case, assuming that the objects follow low-degree al- gebraic trajectories. The full paper [1] presents ad- ditional results for convex fat 3-dimensional objects that are free-flying in R3
Kinetic and Dynamic Delaunay tetrahedralizations in three dimensions
We describe the implementation of algorithms to construct and maintain
three-dimensional dynamic Delaunay triangulations with kinetic vertices using a
three-simplex data structure. The code is capable of constructing the geometric
dual, the Voronoi or Dirichlet tessellation. Initially, a given list of points
is triangulated. Time evolution of the triangulation is not only governed by
kinetic vertices but also by a changing number of vertices. We use
three-dimensional simplex flip algorithms, a stochastic visibility walk
algorithm for point location and in addition, we propose a new simple method of
deleting vertices from an existing three-dimensional Delaunay triangulation
while maintaining the Delaunay property. The dual Dirichlet tessellation can be
used to solve differential equations on an irregular grid, to define partitions
in cell tissue simulations, for collision detection etc.Comment: 29 pg (preprint), 12 figures, 1 table Title changed (mainly
nomenclature), referee suggestions included, typos corrected, bibliography
update
A robust potential-based contact force solution approach for discontinuous deformation analysis of irregular convex polygonal block/particle systems
Contact interaction of two bodies can be modeled using the penalty function approach while its accuracy and robustness are directly associated with the geometry of contact bodies. Particularly, in the research fields of rock mechanics, we need to treat polygonal shapes such as mineral grains/particles at a mesoscale and rock blocks at a macroscale. The irregular shapes (e.g., polygons with small angles or small edges) pose challenges to traditional contact solution approach in terms of algorithmic robustness and complexity. This paper proposed a robust potential-based penalty function approach to solve contact of polygonal particles/block. An improved potential function is proposed considering irregular polygonal shapes. A contact detection procedure based on the entrance block concept is presented, followed by a numerical integral algorithm to compute the contact force. The proposed contact detection approach is implemented into discontinuous deformation analysis with an explicit formulation. The accuracy and robustness of the proposed contact detection approach are verified by benchmarking examples. The potential of the proposed approach in analysis of kinetic behavior of complex polygonal block systems is shown by two application examples. It can be applied in any discontinuous computation models using stepwise contact force-based solution procedures. © 2020, The Author(s)
Molecular dynamics of arbitrarily shaped granular particles}
We propose a new model for the description of complex granular particles and
their interaction in molecular dynamics simulations of granular material in two
dimensions. The grains are composed of triangles which are connected by
deformable beams. Particles are allowed to be convex or concave. We present
first results of simulations using this particle model.Comment: uuencoded compressed PostScript, 40 pages, 19 figures (included
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